To show the graph, you would plot the Cost and Revenue functions on a coordinate plane.
Step 1: Set up the axes.
• The horizontal axis (x-axis) represents the Number of Bottles Produced and Sold.
• The vertical axis (y-axis) represents Total Cost/Revenue (₦).
Step 2: Plot the Cost Function C(x)=10,000+0.03x.
• This is a straight line.
• Y-intercept (Fixed Cost): When x=0, C(0)=10,000. Plot the point (0,10,000).
• Cost at Maximum Annual Capacity: When x=600,000, C(600,000)=10,000+0.03×600,000=28,000. Plot the point (600,000,28,000).
• Draw a straight line connecting these two points.
Step 3: Plot the Revenue Function R(x)=0.46x.
• This is also a straight line.
• Origin: When x=0, R(0)=0. Plot the point (0,0).
• Revenue at Maximum Annual Capacity: When x=600,000, R(600,000)=0.46×600,000=276,000. Plot the point (600,000,276,000).
• Draw a straight line connecting these two points.
Step 4: Identify the Break-Even Point.
• The break-even point is where the Cost line and the Revenue line intersect.
• From the previous calculation, the break-even point is approximately (23,256bottles,₦10,697.76). Mark this intersection point on your graph.
Description of the Graph:
You will see two straight lines originating from the y-axis.
• The Cost line starts at ₦10,000 on the y-axis and slopes upwards.
• The Revenue line starts at ₦0 (the origin) and slopes upwards more steeply than the cost line.
• The point where these two lines cross is the break-even point. To the left of this point, the cost line is above the revenue line, indicating a loss. To the right of this point, the revenue line is above the cost line, indicating a profit.